1. What is Spherical to Rectangular Conversion?

The spherical to rectangular coordinate conversion transforms coordinates from the spherical system (r, θ, φ) to the Cartesian system (x, y, z). This is essential in physics, engineering, and computer graphics where different coordinate systems are used for different applications.

2. How Does the Calculator Work?

The calculator uses the following equations:

Where:

• \( r \) — Radial distance from origin (meters)
• \( \theta \) — Azimuthal angle in the x-y plane from x-axis (radians)
• \( \phi \) — Polar angle from z-axis (radians)

Explanation: These equations project the spherical coordinates onto the three perpendicular axes of the Cartesian system.

3. Applications of Coordinate Conversion

Details: Coordinate conversion is used in 3D graphics, physics simulations, antenna design, satellite tracking, and navigation systems where different coordinate systems are more natural for different aspects of the problem.

4. Using the Calculator

Tips: Enter radial distance (r > 0), azimuthal angle (θ), and polar angle (φ) in radians. The calculator will output the corresponding x, y, z Cartesian coordinates.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between spherical and rectangular coordinates?
A: Spherical coordinates describe points with distance and two angles, while rectangular coordinates use three perpendicular distances.

Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180. Many calculators have a degree-to-radian conversion function.

Q3: What are typical ranges for the angles?
A: θ typically ranges from 0 to 2π (0° to 360°), φ ranges from 0 to π (0° to 180°).

Q4: Can I use negative radial distance?
A: While mathematically possible, physically r is always non-negative in most applications.

Q5: When would I use spherical coordinates?
A: Spherical coordinates are natural for problems with spherical symmetry, like planetary motion or radiation patterns.